Given the following marks of 40 students, construct a frequency distribution table and draw a cumulative frequency curve.

Here are the steps to solve the problem:

Step 1: Organize the raw data.
The marks obtained by 40 students are:
51, 46, 38, 68, 21, 51, 58, 64, 72, 33, 86, 48, 67, 93, 71, 63, 44, 50, 22, 91, 78, 66, 52, 81, 43, 64, 53, 82, 45, 58, 57, 72, 62, 77, 61, 74, 88, 35, 43, 56.

Sorting the data in ascending order:
21, 22, 33, 35, 38, 43, 43, 44, 45, 46, 48, 50, 51, 51, 52, 53, 56, 57, 58, 58, 61, 62, 63, 64, 64, 66, 67, 68, 71, 72, 72, 74, 77, 78, 81, 82, 86, 88, 91, 93.

a) Construct a frequency distribution table.
Using class intervals of 20-29, 30-39, 40-49, etc.:

Class Interval	Frequency (f)	Cumulative Frequency (cf)
20-29	2	2
30-39	3	5
40-49	6	11
50-59	9	20
60-69	8	28
70-79	6	34
80-89	4	38
90-99	2	40
Total	40

b) Draw a cumulative frequency curve for the distribution.
To draw the cumulative frequency curve (ogive), plot the cumulative frequency against the upper class boundaries.
The upper class boundaries are 29.5, 39.5, 49.5, 5